English Title

On the determination of series, or a new method for finding the general terms of series

Authors

Leonhard Euler

Enestrom Number

189

Fuss Index

124

Original Language

Latin

Published as

Journal article

Published Date

1753

Written Date

1749

Content Summary

This paper attempts to determine f(x), given f(1), f(2), f(3), etc. Euler begins with the example f(n) = n and tries f(x) = x + b1∙sin(π x) + b2∙sin(2π x) + b3∙sin(3π x) + .... Note that f(x) – x must be periodic, with f(x+1) = f(x). Then he gets f(x+1) by Taylor series at f(x) and obtains a differential equation of infinite order. A few paragraphs later, we have a perfect Fourier series.

Original Source Citation

Novi Commentarii academiae scientiarum Petropolitanae, Volume 3, pp. 36-85.

Opera Omnia Citation

Series 1, Volume 14, pp.463-515.

Record Created

2018-09-25

E189-a(36-61).pdf (6768 kB)
E189-b(62-85).pdf (6181 kB)
E189-a(36-61).pdf (6768 kB)

E189-b(62-85).pdf (6181 kB)

Included in

Mathematics Commons

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